CN108919837A - A kind of dynamic (dynamical) automatic driving vehicle Second Order Sliding Mode Control method of view-based access control model - Google Patents
A kind of dynamic (dynamical) automatic driving vehicle Second Order Sliding Mode Control method of view-based access control model Download PDFInfo
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Abstract
The invention discloses a kind of dynamic (dynamical) automatic driving vehicle Second Order Sliding Mode Control methods of view-based access control model, belong to intelligent vehicle field.It initially sets up two degrees of freedom vehicle lateral dynamic model and Visual Dynamics model and merges, the curvature ρ for taking aim at an expected path in advance is inputted as external disturbance, reassembles into vehicle dynamic model；And according to the actual shifts distance y before vehicle course between viewpoint and expected pathLAnd the practical tangential angle ε between vehicle course and expected pathL, design the control law of single order sliding mode controller；On the basis of the control law of single order sliding mode controller, by reconstructing sliding variable s, the control law u of super-twisting Second Order Sliding Mode Control device is obtainedsThe value range of middle weighting coefficient λ and α；The value range of weighting coefficient λ and α are applied to the control law u of Second Order Sliding Mode Control devicesIn, realize the automatic Pilot of vehicle.The present invention solves in Survey on Nonlinear System Control, and traditional sliding formwork control is discontinuous, has a series of problems, such as buffeting, has stronger robustness.
Description
Technical Field
The invention relates to a second-order sliding mode control method of an automatic driving vehicle based on visual dynamics, and belongs to the field of intelligent vehicles.
Background
With the development and progress of society, intelligent vehicles are becoming more and more concerned, and due to the potential value and the application prospect in the future, various researches on intelligent vehicles are continuously carried out. Meanwhile, the application of emerging technologies such as laser radar, computer vision and GPS in the field of intelligent vehicles promotes the research on the control strategy of the intelligent vehicle based on path perception.
The path perception is to use the existing sensor technology to sense and plan the path to be traveled by the vehicle in advance, generate a vehicle travel expected path, then input the parameters of the path into a vehicle controller, and complete the tracking travel of the expected path by controlling the front wheel turning angle and the travel speed of the vehicle.
Therefore, a control algorithm with fast response, precise control, and strong robustness is a key step in completing path tracking. Currently existing control algorithms are: a feedback control strategy, a PID control strategy, a sliding mode control strategy, an optimal control strategy and the like. As in document [1 ]: jiana applied to a vision system lateral control strategy [ J ],1999,18(5): 1903-. Document [2 ]: wang Kundong, automobile stabilization system sliding mode control based on road surface identification [ J ] automobile engineering, 2018(1) 82-90, and an LQR optimal state regulator is designed by taking minimized transverse pre-aiming error and deviation between a vehicle and a target path as control targets. The document [3] Guojinghua, Lelinhui, a transverse adaptive fuzzy sliding mode control strategy [ J ] of an automatic vehicle based on visual course A vehicle power system, 2013,51(10):1502 and 1517 propose an adaptive fuzzy sliding mode control strategy for overcoming the nonlinear characteristics, parameter uncertainty and external interference of transverse control. However, the above prior art documents have the following disadvantages: the traditional linear control strategy cannot well cope with the running condition which changes in real time; and does not have good robustness; the first-order sliding mode control can generate strong buffeting when the working condition is changed; while not allowing continuous control over varying operating conditions.
Disclosure of Invention
In order to solve the problems, the invention provides a second-order sliding mode control method of an automatic driving vehicle based on visual dynamics, compared with the traditional first-order sliding mode, a super-twisting second-order sliding mode control strategy can more effectively achieve the control purpose and inhibit the generation of buffeting.
The method comprises the following specific steps:
the method comprises the following steps that firstly, a two-degree-of-freedom vehicle lateral dynamics model and a visual dynamics model are established for a certain vehicle running on a good road surface;
the two-degree-of-freedom vehicle lateral dynamics model is as follows:
cfas stiffness of the front wheel, crIs the stiffness of the rear wheel, m is the vehicle mass, vxFor the longitudinal running speed v of the vehicleyThe transverse running speed of the vehicle; r represents a vehicle yaw rate, δfIndicating the angle of rotation of the front wheels of the vehicle, IzRepresenting the yaw moment of inertia, l, of the vehiclefIs the distance from the center of mass of the vehicle to the front axle,/rIs the distance from the center of mass of the vehicle to the rear axle.
The visual dynamics model of unmanned driving is as follows:
yLrepresenting the actual offset distance, ε, between the vehicle heading front point and the desired pathLAnd the actual tangential included angle between the heading of the vehicle and the expected path is shown, L is the pre-aiming distance of the vehicle sensor, and rho is the curvature of the expected path of the pre-aiming point.
Combining a two-degree-of-freedom vehicle lateral dynamics model and a visual dynamics model, and recombining a curvature rho of an expected path of a pre-aiming point as external disturbance input into a vehicle dynamics model suitable for unmanned driving;
the equation of state of the vehicle dynamics model is as follows:
wherein
Thirdly, according to the actual offset distance y between the vehicle heading front point and the expected path in the vehicle dynamic modelLAnd the actual tangential angle epsilon between the vehicle heading and the desired pathLDesigning a control law of a first-order sliding mode controller;
the equation for the control law u is as follows:
wherein KrThe intermediate coefficients are the coefficients of the intermediate coefficients,k1、k2respectively are positive constants;
s is a sliding mode variable; s ═ e1；e1＝yL-yd+ξ1(εL-εd)，ydFor a desired offset distance between a forward point of view and a desired path of the vehicle, ξ1Is a positive weighting coefficient representing an error e of one relative order1In the difference pair of the actual and ideal tangential included anglese1The influence ratio of (1); epsilondIs the desired tangential angle between the vehicle heading and the desired path.
Step four, on the basis of the control law of the first-order sliding mode controller, the control law u of the super-twisting second-order sliding mode controller is obtained by reconstructing the sliding mode variable ssThe value ranges of the medium weighting coefficients lambda and α;
the method comprises the following specific steps:
step 401, reconstructing a sliding mode variable of a second-order sliding mode system on the basis of a first-order sliding mode variable s;
s'＝ce1+e2
where c is a positive weighting coefficient representing the error e with a relative order of one1Weight to the entire slip form face; at the same timeξ2And ξ1Similarly, it represents the error e in the relative order of two2In the pair of differences e of the first derivatives of the actual and ideal tangential angles2The influence ratio of (1);
step 402, taking external disturbance input rho as a control law u of a second-order sliding mode controllersIntroducing a first derivative relation of a second-order sliding mode variable, and simultaneously using intermediate variables omega and KvSimplifying the process;
the first derivative relationship is as follows:
wherein,
Kv＝b1+b2L；
control law u of second-order sliding mode controllersThe formula is as follows:
λ and α are weighting coefficients, respectively, s' (t) is a time function of the sliding mode variable;
step 403, combine the actual offset distance yLTrue tangential angle epsilonLDesired offset distance ydAnd desired tangential angle εdThe intermediate variable omega of the first derivative relational expression of the second-order sliding mode variable is transformed;
because a positive constant theta and a sliding mode variable s at a specific moment always exist, the transformation formula is as follows:
ω＝θ|s|1/2sign(s)
step 404, performing primary transformation on a first derivative relational expression of the second-order sliding mode variable, reconstructing the sliding mode variable and a state equation, and obtaining transition matrixes A and omega;
τ1＝Kvλ,τ2＝Kvα
carrying out mathematical change on the first derivative of the second-order sliding mode variable and reconstructing the first derivative to obtain an intermediate matrixAnd its first derivative, as follows:
wherein,as an intermediate matrixThe first element of (1);as an intermediate matrixThe second element of (1).
By adding the transition matrices A and omega, the intermediate matrix is addedFirst derivative ofRe-expression gave:
step 405, calculating a quadratic-like Lyapunov function V and a first derivative thereof by combining the transition matrix A and the transition matrix omega;
selecting a Lyapunov function as follows:p is the selected positive definite matrix;
the first derivative of the Lyapunov function is as follows:
by simplification, the matrix Q in the above formula is:
step 406, calculating a second-order sliding mode control law u on the premise of meeting the system stability conditionsThe value ranges of the medium weighting coefficients lambda and α;
the system stability conditions were: lyapunov function V>0, and the first derivative of the Lyapunov functionThen the matrix Q should be positive definite matrix at this time, i.e. Q>0；
Obtaining the positive timing of Q according to the property of Schulk's complement, the state of the system can be converged to the origin in a limited time, and obtaining the value ranges of parameters lambda and α according to the stability condition of the system as follows:
step five, applying the value ranges of the weighting coefficients lambda and α to the control law u of the second-order sliding mode controllersIn the above, automatic driving of the vehicle is realized.
The invention has the advantages that:
1) a second-order sliding mode control method of an automatic driving vehicle based on visual dynamics can better solve the nonlinear system control theory and enable the vehicle to have a better control effect under the condition of disturbance and uncertainty conditions
2) A second-order sliding mode control method of an automatic driving vehicle based on visual dynamics can be effectively used for eliminating buffeting caused by first-order sliding modes and making up for the defect that the relative order is one, and therefore the system has strong robustness.
3) A second-order sliding mode control method of an automatic driving vehicle based on visual dynamics can compensate uncertainty of Lipschitz, and control effect can be achieved only by information of a sliding variable, so that the vehicle can follow a target track more flexibly and accurately.
4) A second-order sliding mode control method of an automatic driving vehicle based on visual dynamics can enable a sliding variable and a time derivative thereof to be converged at an original point at the same time in limited time and generate continuous control signals, so that the vehicle can track a target track more smoothly.
Drawings
FIG. 1 is a schematic diagram of a second order sliding mode control for an autonomous vehicle based on visual dynamics in accordance with the present invention;
FIG. 2 is a flow chart of a second order sliding mode control method of an autonomous vehicle based on visual dynamics according to the present invention;
FIG. 3 is a two degree of freedom vehicle dynamics model of an autonomous vehicle based on visual dynamics in accordance with the present invention;
FIG. 4 is a visual dynamics model of an autonomous vehicle based on visual dynamics in accordance with the present invention;
FIG. 5 is a flow chart of the value range of weighting coefficients λ and α in the second-order control law obtained by reconstructing a sliding mode variable s according to the present invention;
FIG. 6 is a diagram illustrating a demonstration result obtained from a preset path used in the simulation of the present invention;
FIG. 7a is a simulation comparison graph of a front wheel caster under the SOSM control strategy and the FOSM control strategy of the present invention;
FIG. 7b is a simulated comparison of yaw rate for the SOSM control strategy and the FOSM control strategy of the present invention;
FIG. 7c is a simulated comparison of the true vehicle trajectory for the SOSM control strategy and the FOSM control strategy of the present invention;
Detailed Description
The present invention will be described in further detail below with reference to the accompanying drawings.
The invention develops research on the aspect of sliding mode controllers of unmanned vehicles based on a known path. According to the dynamic state of the intelligent vehicle in actual operation, visual dynamics is combined with a two-degree-of-freedom vehicle dynamics model, and a first-order sliding mode controller is designed to enable the lateral deviation and the azimuth deviation of a front viewpoint to reach an ideal state. The front wheel steering angle to correct the vehicle condition is then derived and used as an input to control the vehicle to track the desired path steadily. And finally, designing a control strategy of a super-twisting second-order sliding mode to eliminate the buffeting problem caused by the first-order sliding mode.
As shown in fig. 1, firstly, briefly analyzing a two-degree-of-freedom vehicle dynamics model, and introducing a vehicle coordinate system visual dynamics model based on path perception according to a path perception sensor; designing a controller of a first-order sliding mode and super-twisting second-order system, carrying out a Carsim/Simulink combined simulation experiment on different control algorithms, and verifying the effectiveness of the proposed control strategy, thereby obtaining a final conclusion.
As shown in fig. 2, the specific steps are as follows:
the method comprises the following steps that firstly, a two-degree-of-freedom vehicle lateral dynamics model and a visual dynamics model are established for a certain vehicle running on a good road surface;
a vehicle coordinate system path tracking model is established, a two-degree-of-freedom vehicle dynamic model is firstly given, a visual dynamic model is introduced and fused, and finally the model is applied to the problem to be solved.
When the vehicle runs on a road surface with good adhesion, the linear two-degree-of-freedom model can well represent the running characteristic and the operating characteristic of the vehicle. Therefore, the present invention adopts a two-degree-of-freedom bicycle dynamics model for the subsequent controller design, which is shown in fig. 3:
the two-degree-of-freedom vehicle lateral dynamics model is expressed by the following equation set:
cfas stiffness of the front wheel, crFor the rigidity of the rear wheels, c in this modelfAnd crIs an ideal constant value. m is the total vehicle mass, vxFor the longitudinal running speed v of the vehicleyThe transverse running speed of the vehicle; r represents a vehicle yaw rate, δfIndicating the angle of rotation of the front wheels of the vehicle, IzRepresenting the yaw moment of inertia, l, of the vehiclefIs the distance from the center of mass of the vehicle to the front axle,/rIs the distance from the center of mass of the vehicle to the rear axle.
In order to enable the unmanned vehicle to truly simulate the driving habit of a driver, an unmanned visual dynamic model is introduced, the model is a geometric relation between a body posture at a certain position and a desired road in a vehicle coordinate system according to desired path information captured by a sensor in real time, and as shown in fig. 4, the formula is as follows:
yLrepresenting the actual offset distance, ε, between the vehicle heading front point and the desired pathLAnd the actual tangential included angle between the heading of the vehicle and the expected path is shown, L is the pre-aiming distance of the vehicle sensor, and rho is the curvature of the expected path of the pre-aiming point.
Combining a two-degree-of-freedom vehicle lateral dynamics model and a visual dynamics model, and recombining a curvature rho of an expected path of a pre-aiming point as external disturbance input into a vehicle coordinate system path tracking model suitable for unmanned driving;
the equation of state of the vehicle dynamics model is as follows:
wherein
And in the equation of state, the state variableControl input u-deltafAnd the external disturbance ω is ρ.
Thirdly, according to the actual offset distance y between the vehicle heading front point and the expected path in the vehicle dynamic modelLAnd the actual tangential angle epsilon between the vehicle heading and the desired pathLDesigning a control law of a first-order sliding mode controller;
through the development of decades, the first-order sliding mode control becomes a theory capable of better solving the control of a nonlinear system, and under the condition of disturbance and uncertainty conditions, a closed-loop system has a better control effect. However, the first-order sliding mode control is easy to generate buffeting, and the defect that the relative order is one limits the application field and the development prospect of the first-order sliding mode control.
Since the objective of the study is to perform dynamic control of the vehicle based on the geometric state between the pre-aim point and the vehicle attitude, the actual distance y between the pre-aim point and the desired path of the vehicle heading can be usedLAnd the tangential angle epsilon between the vehicle heading and the desired pathLA sliding mode surface of a first-order sliding mode controller is designed, and the equation is as follows:
s＝yL-yd+ξ1(εL-εd) (4)
ξ1the weighting coefficient is a positive value and represents the influence proportion of the tangential included angle to the whole sliding mode surface in an error e1 with a relative order of one; y isdA desired offset distance between a forward-looking point and a desired path for the vehicle heading; epsilondIs the desired tangential angle between the vehicle heading and the desired path.
Differentiating equation (4) yields:
wherein KrThe intermediate coefficients are the coefficients of the intermediate coefficients,due to tangential included angle epsilonLThe change is very slow and ω (t) is bounded, the desired distance ydAnd desired tangential angle εdIs derived from the preview pathThe same description as aboveIs a bounded variable, then there is a constantSo thatIn summary, the following first-order sliding mode control algorithm can be obtained:
k1、k2respectively are positive constants; when in useAnd has k2>At 0, the state of equation (4) may converge to the origin within a finite time.
The following was demonstrated: substituting equation (6) into equation (5) yields:
selecting Lyapunov functionAnd substituting the formula (7) and then obtaining the derivation:
when in useAnd has k2>At the time of 0, the number of the first,the state convergence of the formula (4) can be obtained by the Lyapunov stability theory.
Step four, on the basis of the control law of the first-order sliding mode controller, the control law u of the super-twisting second-order sliding mode controller is obtained by reconstructing the sliding mode variable ssThe value ranges of the medium weighting coefficients lambda and α;
the Super-twisting second-order sliding mode control can effectively solve the buffeting defect of the traditional sliding mode system and make up the defect that the relative order is one, and has the obvious advantages that: the method can compensate for the uncertainty of Lipschitz and it requires only information of the sliding variables. Meanwhile, the sliding variable and the time derivative thereof can be converged to the origin point at the same time in a limited time, a continuous control signal is generated, and the occurrence of buffeting is suppressed.
As shown in fig. 5, the specific steps are as follows:
step 401, reconstructing a sliding mode variable of a second-order sliding mode system on the basis of a first-order sliding mode variable s;
s'＝ce1+e2(9)
wherein e1Is a sliding mode variable s; c is a positive weighting coefficient representing the error e with a relative order of one1The influence ratio on the whole sliding mode surface; at the same timeξ2And ξ1Similarly, a positive weighting factor represents an error e in the relative order of two2Influence proportion of the middle tangential included angle;
step 402, taking external disturbance input rho as a control law u of a second-order sliding mode controllersIntroducing a first derivative relation of a second-order sliding mode variable, and simultaneously using intermediate variables omega and KvSimplifying the process;
according to the combination of the state equation (3) and the sliding mode variable (9) of the reconstructed second-order sliding mode system, the method can be obtained
The first derivative relationship is as follows:
wherein,
Kv＝b1+b2L；
control law u of second-order sliding mode controllersThe formula is as follows:
λ and α are weighting coefficients, respectively, s' (t) is a time function of the sliding mode variable;
step 403, combine the actual offset distance yLTrue tangential angle epsilonLDesired offset distance ydAnd desired tangential angle εdThe intermediate variable omega of the first derivative relational expression of the second-order sliding mode variable is transformed;
due to the actual offset distance yLTrue tangential angle epsilonLThe change is very slow and bounded, the desired offset distance ydAnd desired tangential angle εdIs derived from the preview path, again accounting for the desired offset distance ydAnd desired tangential angle εdFirst and second reciprocal ofIs a bounded variable, then there is a positive constant theta and a sliding mode variable s at a specific time, so that omega satisfies
ω＝θ|s|1/2sign(s) (12)
Step 404, performing primary transformation on a first derivative relational expression of the second-order sliding mode variable, reconstructing the sliding mode variable and a state equation, and obtaining transition matrixes A and omega;
control law u of second-order sliding mode controllersThe formula (11) of (a) is expressed in the following form:
τ1＝Kvλ,τ2＝Kvα
simplifying a first derivative (13) formula of a second-order sliding mode variable, and differentiating the first-order derivative to obtain an intermediate matrixAnd its first derivative, as follows:
wherein,as an intermediate matrixThe first element of (1);as an intermediate matrixThe second element of (1).
By adding the transition matrices A and omega, the intermediate matrix is addedFirst derivative ofRe-expression gave:
step 405, calculating a quadratic-like Lyapunov function V and a first derivative thereof by combining the transition matrix A and the transition matrix omega;
choosing a Lyapunov function as:
p is the selected positive definite matrix;so that V>0。
Derivation of the Lyapunov function equation (18) along the trajectory of equation (9) and substitution of equations (12) and (17) results in the first derivative of the Lyapunov function as follows:
by simplification, the matrix Q in the above formula is:
step 406, calculating a second-order sliding mode control law u on the premise of meeting the system stability conditionsThe value ranges of the medium weighting coefficients lambda and α;
the system stability conditions were: lyapunov function V>0, and the first derivative of the Lyapunov functionThen the matrix Q should be positive definite matrix at this time, i.e. Q>0；
Obtaining the positive timing of Q according to the property of Schulk complement, stabilizing the state of the system, converging the sliding mode variable to the original point in limited time, and obtaining the value ranges of parameters lambda and α according to the stability condition of the system as follows:
step five, applying the value ranges of the weighting coefficients lambda and α to the control law u of the second-order sliding mode controllersIn the above, automatic driving of the vehicle is realized.
Simulation results and analysis:
in order to check the effectiveness of the control strategy, the invention establishes a simulation model in Carsim/Simulink and sets the changed road conditions; and comparing the control effects of the two control strategies. The vehicle parameters are shown in table 1:
TABLE 1
The expected path taken by the simulation is shown in figure 6,
FIG. 7 shows the results of comparing the transient response of the Super-twining SOSM control strategy and the FOSM control strategy. As shown in FIGS. 7a and 7b, the FOSM control strategy can generate continuous buffeting when the system state changes suddenly, and the Super-twisting SOSM control strategy has better stability. As can be seen from fig. 7c, the Super-twining SOSM control strategy has faster tracking performance, although the FOSM also has some follow-up on the target desired path.
Claims (2)
1. A second-order sliding mode control method of an automatic driving vehicle based on visual dynamics is characterized by comprising the following specific steps:
the method comprises the following steps that firstly, a two-degree-of-freedom vehicle lateral dynamics model and a visual dynamics model are established for a certain vehicle running on a good road surface;
the two-degree-of-freedom vehicle lateral dynamics model is as follows:
cfas stiffness of the front wheel, crIs the stiffness of the rear wheel, m is the vehicle mass, vxFor the longitudinal running speed v of the vehicleyThe transverse running speed of the vehicle; r represents a vehicle yaw rate, δfIndicating the angle of rotation of the front wheels of the vehicle, IzRepresenting the yaw moment of inertia, l, of the vehiclefIs the distance from the center of mass of the vehicle to the front axle,/rThe distance from the center of mass of the vehicle to the rear axle;
the visual dynamics model of unmanned driving is as follows:
yLrepresenting the actual offset distance, ε, between the vehicle heading front point and the desired pathLRepresenting an actual tangential included angle between the vehicle course and the expected path, wherein L is the pre-aiming distance of a vehicle sensor, and rho is the curvature of the expected path of a pre-aiming point;
combining a two-degree-of-freedom vehicle lateral dynamics model and a visual dynamics model, and recombining a curvature rho of an expected path of a pre-aiming point as external disturbance input into a vehicle dynamics model suitable for unmanned driving;
the equation of state of the vehicle dynamics model is as follows:
wherein
Thirdly, according to the actual offset distance y between the vehicle heading front point and the expected path in the vehicle dynamic modelLAnd the actual tangential angle epsilon between the vehicle heading and the desired pathLDesigning a control law of a first-order sliding mode controller;
the equation for the control law u is as follows:
wherein KrThe intermediate coefficients are the coefficients of the intermediate coefficients,k1、k2respectively are positive constants;
s is a sliding mode variable; s ═ e1；e1＝yL-yd+ξ1(εL-εd)，ydFor a desired offset distance between a forward point of view and a desired path of the vehicle, ξ1Is a positive weighting coefficient representing an error e of one relative order1In the pair of difference e between the actual and ideal tangential angles1The influence ratio of (1); epsilondThe expected tangential included angle between the heading of the vehicle and the expected path;
step four, on the basis of the control law of the first-order sliding mode controller, the control law u of the super-twisting second-order sliding mode controller is obtained by reconstructing the sliding mode variable ssThe value ranges of the medium weighting coefficients lambda and α;
the method comprises the following specific steps:
step 401, reconstructing a sliding mode variable of a second-order sliding mode system on the basis of a first-order sliding mode variable s;
s'＝ce1+e2
where c is a positive weighting coefficient representing the error e with a relative order of one1Weight to the entire slip form face; at the same timeξ2And ξ1Similarly, it represents the error e in the relative order of two2In the pair of differences e of the first derivatives of the actual and ideal tangential angles2The influence ratio of (1);
step 402, taking external disturbance input rho as a control law u of a second-order sliding mode controllersIntroducing a first derivative relation of a second-order sliding mode variable, and simultaneously using intermediate variables omega and KvSimplifying the process;
the first derivative relationship is as follows:
wherein,
Kv＝b1+b2L；
control law u of second-order sliding mode controllersThe formula is as follows:
λ and α are weighting coefficients, respectively, s' (t) is a time function of the sliding mode variable;
step 403, combine the actual offset distance yLTrue tangential angle epsilonLDesired offset distance ydAnd desired tangential angle εdThe intermediate variable omega of the first derivative relational expression of the second-order sliding mode variable is transformed;
because a positive constant theta and a sliding mode variable s at a specific moment always exist, the transformation formula is as follows:
ω＝θ|s|1/2sign(s)
step 404, performing primary transformation on a first derivative relational expression of the second-order sliding mode variable, reconstructing the sliding mode variable and a state equation, and obtaining transition matrixes A and omega;
τ1＝Kvλ,τ2＝Kvα
carrying out mathematical change on the first derivative of the second-order sliding mode variable and reconstructing the first derivative to obtain an intermediate matrixAnd its first derivative, as follows:
wherein,as an intermediate matrixThe first element of (1);as an intermediate matrixThe second element of (1);
by adding the transition matrices A and omega, the intermediate matrix is addedFirst derivative ofRe-expression gave:
step 405, calculating a quadratic-like Lyapunov function V and a first derivative thereof by combining the transition matrix A and the transition matrix omega;
selecting a Lyapunov function as follows:p is the selected positive definite matrix;
the first derivative of the Lyapunov function is as follows:
by simplification, the matrix Q in the above formula is:
step 406, calculating a second-order sliding mode control law u on the premise of meeting the system stability conditionsThe value ranges of the medium weighting coefficients lambda and α;
obtaining the positive timing of Q according to the property of Schulk's complement, the state of the system can be converged to the origin in a limited time, and obtaining the value ranges of parameters lambda and α according to the stability condition of the system as follows:
step five, applying the value ranges of the weighting coefficients lambda and α to the control law u of the second-order sliding mode controllersIn the above, automatic driving of the vehicle is realized.
2. The second order sliding mode control method for automatic driving vehicle based on visual dynamics as claimed in claim 1, wherein the system stability condition in step 406 is: lyapunov function V>0, and the first derivative of the Lyapunov functionThen the matrix Q should be positive definite matrix at this time, i.e. Q>0。
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| CN110471277A (en) * | 2019-07-22 | 2019-11-19 | 清华大学 | Intelligent commercial vehicle automatic tracking control method based on output feedback oscillator planning |
| CN110568758B (en) * | 2019-09-12 | 2022-07-01 | 中汽研（天津）汽车工程研究院有限公司 | Parameter self-adaptive transverse motion LQR control method for automatically driving automobile |
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| CN111703417A (en) * | 2020-06-24 | 2020-09-25 | 湖北汽车工业学院 | High-low speed unified preview sliding mode driving control method and control system |
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| CN112193236A (en) * | 2020-09-11 | 2021-01-08 | 江苏大学 | Second-order sliding mode anti-collision control method based on active steering and yaw moment control |
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| WO2024179024A1 (en) * | 2023-02-27 | 2024-09-06 | 东南大学 | Motion path planning and adaptive lateral control method for driverless vehicle |
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